Additive noise, Weibull functions and the approximation of psychometric functions

Area of Science:

• Psychophysics
• Sensory neuroscience
• Mathematical modeling

Background:

• The Weibull function is commonly used for psychometric functions.
• Tyler and Chen (2000) criticized its implied high-threshold and multiplicative noise assumptions.

Purpose of the Study:

• To re-evaluate the Weibull function's compatibility with noise assumptions.
• To generalize the Weibull function for non-high-threshold detection.
• To propose a more general model for sensory activity.

Main Methods:

• Derivations based on sensory activity representations.
• Modeling detection as a level-crossing process using stochastic processes.
• Considering additive, stationary Gaussian noise and cascaded Poisson processes (multiplicative noise).

Main Results:

• The Weibull function is compatible with additive noise and generalized detection.
• Weibull functions approximate psychometric functions from both additive and multiplicative noise models.
• Parameters of fitted Weibull functions lack simple interpretation.
• Multiplicative noise sources are compatible with the Weibull function.

Conclusions:

• The Weibull function is more flexible regarding noise and thresholds than previously suggested.
• A generalized level-crossing model provides a broader framework for sensory detection.
• While Weibull functions approximate various noise types, their parameters are not straightforwardly interpretable.
• Multiplicative noise might play a minor role in many sensory detection tasks.